Let \(V\)  be a centrally symmetric (with respect to the origin)
closed
convex body in \({\mathbb {R}}^m\)  and
\(V^*:=\lbrace y\in {\mathbb {R}}^m: \forall \, t\in V, \vert t\cdot y\vert \le 1\rbrace \) 
be the polar of \(V\) .
It is well known that \(V^*\)  is a centrally symmetric (with respect to the origin)
closed
convex body in \({\mathbb {R}}^m\)  and \(V^{**} =V\)  (see, e.g., [1]}).
The set \(V\)  generates the following dual norms
on \({\mathbb {R}}^m\)  and \({\mathbb {C}}^m\)  by
\(\Vert y\Vert _V^*:=\sup _{t\in V}\vert t\cdot y\vert ,\quad y\in {\mathbb {R}}^m;\qquad \Vert z\Vert _V^*:=\sup _{t\in V}\left|\sum _{j=1}^m t_jz_j\right|,\quad z\in {\mathbb {C}}^m.\) 
